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C3×C23×C11⋊Dic11 #45688993

order33396
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C11

Aliases

direct productC3×C23×C11⋊Dic11
unambiguous semidirect productC11⋊(C3×C23×Dic11)

Splittings

derived, SylowC112 ⋊ C3×C4×C23
HallC3×C112×C23 ⋊ C4
HallC112×C23 ⋊ C3×C4
HallC3×C112 ⋊ C4×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23C11⋊D11
commutator, hypocenterC112C3×C4×C23
FrattiniC2C3×C23×C11⋊D11
Fitting, socle, prime radicalC2×C3×C112×C23C2
cosocleC2×C112C2×C3×C23
LCSG ▷ C112
UCSC1 ◁ C2×C3×C23

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33396

Conjugacy classes & character table

8556 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33396, 57);